The usefulness of a laser often is dependent upon its output wavefront quality, since this determines the degree to which the beam may be focused. The wavefront quality of a laser system depends on the optical quality of all components in the optical train, including the laser media, the resonator optics and any relay or transport optics. The transient nature of the wavefront error is also important because the laser media index of refraction can vary significantly through temperature and flow effects. Furthermore, vibration, modal bending and other random events can affect the beam transport optics. Wavefront quality can be used to measure quantities of interest in incoherent and non-laser systems. In many flow systems, turbulence and macroscopic flow parameters can be measured by inferring the density from the index of refraction. For incompressible flow, the temperature may be inferred from such measurements.
In these applications time-dependent optical wavefront quality measurements are important. The measurements need considerable spatial and temporal resolution, and data analysis and reduction must be automatic.
In addition, other applications of a wavefront sensor include measuring the shape of objects such as disc drive platens and thin films during manufacture.
The Hartmann measurement technique was initially introduced using an opaque plate with several openings to mask the beam. It was used to diagnose imperfections in large telescopes by observing the position of each beam as it propagates through the optical system. Any deviations from the ideal path were attributed to optical imperfections or misalignment.
A common implementation of the Hartmann or Hartmann-Shack technique relies on measuring a change of spot position on a focal plane. By measuring the wavefront slope at different sample positions across the optical aperture, it does not rely on coherence, and inherently has no limit on its dynamic range or resolution. It does not require a reference beam for relative measurements. The invention described in this disclosure is based on a Hartmann technique.
The quantity of data that must be processed for prior art two-dimensional image is significantly greater than for the one-dimensional case of this invention. For scanned detectors, this limits the maximum bandwidth of the wavefront sensor since the maximum pixel rate is the same for both systems. For an N.times.N 2-D detector array operating at R pixel rate (pixels/sec), the wavefront sensor bandwidth is R/N.sup.2. For a 1-D sensor, the bandwidth is R/N. For a 1024 element detector array operating at 20 Megapixels/sec, this corresponds to 20 Hertz bandwidth for 2-D data acquisition, and 19.5 KHz for the 1-D sensor. This increase is a key difference between the invention described here and the prior art since temporal resolution is critical for many applications. To make a two-dimensional wavefront sensor operate at higher bandwidth, the dynamic range, bandwidth or resolution must be reduced.
Shack-Hartmann sensing has been used extensively in optical fabrication and testing, astronomy, adaptive optics, and laser beam control. (D . Acton et al., "Solar imaging with a segmented adaptive mirror," Appl. Optics, 31(16), 3161-3169 (1 Jun. 1992)). The Shack-Hartmann sensor is used to measure the wavefront of a beam of coherent or incoherent light. It consists of an array of lenses that focus onto a detector array capable of measuring the position of the focused light. With the detector at the focal position, the focal spot position is independent of the intensity pattern across the subaperture, and depends only on the average slope of the wavefront. With many subapertures, the incident wavefront may be reconstructed by spatial integration.
For fluid mechanics problems, usually a laser is used to probe the flow under study, with density variations causing perturbations of the index of refraction of the medium. These index of refraction variations in turn lead to variations in the laser wavefront. The Shack-Hartmann sensor is used to determine these variations. Since the index of refraction usually depends strongly on the density of the fluid and only weakly upon temperature, it can be used to measure the density independent of any other variations in the flow.
There have been several recent developments that have made possible the development of useful wavefront sensors. These include the development of fast CCD area and line scan cameras, the development of micro-lens array manufacturing technology, and the improvement in computer data acquisition and processing equipment.
The Acton Shack-Hartmann wavefront sensor, cited above, uses discrete lenslets and quadrant cell detectors to make a limited number of measurements across the field. These sensors have the advantage of extremely high speed because of the many parallel connections, but have significantly reduced dynamic range, are complicated by the large numbers of connections and electronics and usually have limited net resolution. They are useful for closed loop adaptive optics systems where dynamic range is controlled by a deformable mirror. They can be used for fluid mechanics measurements only for either limited dynamic range effects, or in massively complicated adaptive optics facilities.
Another technique is to use a CCD camera coupled to a lenslet array to simplify the construction of the wavefront sensor. This technique is used extensively in astronomy and other adaptive optics (D. Kwo et al., "A Shack-Hartmann wavefront sensor using a binary optic lenslet array," SPIE Vol. 1544, Miniature and Micro-Optics Fabrication and System Applications, 66-74 (1991)). However, as the number of subapertures grows, bandwidth, resolution, dynamic range or dimensionality must be sacrificed. For adaptive optics systems, the deformable mirror can be used to extend the dynamic range, and hence some of these compromises can be avoided. However, a deformable mirror is extremely expensive and complicated, and is not likely to be applied to laboratory fluid mechanics measurements.